It is demonstrated that with rigorous inclusion of diffraction on an intracavity hard aperture the values of the nonlinear differential loss coefficient Gamma (which characterizes the efficiency of Kerr-lens mode locking) are several times higher than in the commonly used simplified approach in which diffraction effects are neglected. Diffraction changes modal properties and causes a faster decrease of mode losses with increasing power than predicted by the traditional approach. With this correction, the discrepancy between the Kerr-lens mode-locking theory and the theoretical estimates of the self-starting condition is substantially decreased.